
\chapter{摘要}

随着我国高速铁路网络的不断完善，客运营业额不断增加，客票销售方案的制定已经成为铁路客运工作中的重要环节。同时，随着新技术的应用，客票销售更加网络化、集中化。然而目前我国铁路客票销售管理水平还有提高的空间：一方面，我国铁路客票销售方案的制定主要依赖管理人员的经验，缺乏理论支持；另一方面，从上世纪九十年代至今，我国铁路一直采用基于运行里程的定价方式，对客运需求的调节作用有限。本文在借鉴航空业收益管理理论的基础上，研究了我国铁路客票销售中票额预分和动态定价的建模与求解方法，具有重要的理论和现实意义。

本文主要内容包括以下几个方面：

(1) 铁路客票销售的建模框架研究

为了考虑旅客购票顺序及其购票行为中的随机性，并且能够表达复杂的铁路客票销售规则，本文提出了由客票销售决策模型，客票销售过程模型和旅客行为模型三部分构成的铁路收益管理问题的基本建模框架。通过应用马尔科夫决策过程理论和离散选择理论，将客票销售决策模型和旅客的购票行为模型有机地结合起来。在问题的求解上，由于模型结构带来了“维数灾难”的问题，本文引入了近似动态规划的技术介绍了求解客票销售决策模型的一般思路。

(2) 票额预分的优化方法研究

票额预分是我国铁路目前广泛采用的客票销售策略，它包含了席位共用、复用等多种客票销售规则。如何通过模型细化表达票额预分机制是解决票额预分优化的重点问题。本文基于建模框架表达票额预分机制，并且考虑了在此基础上的共用分组票额分配问题，采用了遗传算法求解预分优化问题，并引入了基于规则的启发式方法生成问题的初始解。求解的结果通过仿真实验进行验证并且与其它客票销售规则进行了对比。

(3) 基于动态投标价格的高速铁路动态价格问题研究

采用动态价格的手段是铁路客运市场化运营的重要机制，而动态投标价格控制策略是目前主流的动态价格实现手段之一。本文研究了基于动态投标价格的客票销售规则来制定铁路车票的的动态价格。在建模框架的基础上，本文通过引入最优控制问题与值函数近似方法，构建动态规划模型来计算投标价格。在问题的求解上，将问题进行转换和简化，为了解决产生的大规模线性规划问题，提出了动态聚合方法与列生成方法。在这部分研究中，还考虑了旅客的换乘行为并通过数值实验验证了旅客换乘对铁路客票销售收入的影响。

(4) 基于网络模型的铁路动态价格问题研究

对于铁路动态价格问题模型构建，本文还考虑了基于网络的建模方法。即通过状态网络将旅客出行行为和动态价格机制都表达为网络中的路径。通过求解一类网络路径问题，可以得到动态价格策略。针对这类网络路径问题，本文研究了求解它的拉格朗日启发式方法，通过运用拉格朗日函数分解方法和采用带有置信范围的割平面法，该问题可以并行地快速求解。通过数值实验验证了该方法能够减少求解中拉格朗日乘子的震荡，稳定地逼近最优解。

(5) 南广高速铁路案例研究

以南广高铁2016年暑运为背景，本文在不同的需求情境下，按照本文提出的优化方法，通过仿真实验测试了包括票额预分和动态价格在内的不同类型的客票销售规则对客票销售收入的影响。通过对比验证了灵活运用席位存量和动态定价能够显著提高客票销售收入。

\keywords{高速铁路 \quad{}收益管理 \quad{}票额预分 \quad{}动态票价 \quad{}马尔科夫决策过程 \quad{}近似动态规划
\quad{}遗传算法}

\chapter{Abstract}

With the construction of China high-speed railway network, the income
of passenger transportation has been increasing. The ticket sale decisions
have become an important part of railway passenger transportation.
At the same time, with the application of network technology, ticket
reservation is becoming more centralized and real-time. However, there
are some room for improving the management level of railway ticket
sale at present. On the one hand, the ticket sale decision mainly
relies on the experience of staffs and lacks theoretical support.
On the other hand, the price of railway ticket is based on operating
mileage, which is not suitable for the diversified needs of travelers.
Based on the theory and practice of revenue management in airline
industry, this paper studies modeling and solution methods for railway
passenger ticket sale in China, which has important theoretical and
practical significance.

The main contents of this paper include the following aspects:

(1) Research on modeling framework of railway ticket sale problem

In order to consider the randomness of passenger arrival order and
ticket purchase behavior, and to express complex railway seat inventory
control mechanism, this paper proposes a fundamental model framework
for railway revenue management problem, consisting of three parts:
ticket sale decision model, ticket reservation process model and passenger
behavior model. By applying Markovian decision process theory and
discrete selection theory, the ticket reservation decision model and
the passenger's behavior model can be combined. In this framework,
the seat inventory control mechanism is modeled by state transaction
functions, which can be expanded flexibly. In the solution of the
problem, due to the “curse of dimensionality”, this paper introduces
the technique of approximate dynamic programming, and gives the general
approach of ​​solving the parameter adjustment model.

(2) Research on optimization of ticket pre-allocation

The pre-allocation is a widely used type of inventory control in China's
railway. It includes a variety of seat control mechanisms such as
sharing and reusing seat in a train. The key issue of pre-allocation
optimization is to find a refined model to describe the pre-allocation
mechanism. This paper expands the modeling framework to model the
ticket pre-allocation mechanism, and then considers ticket allocation
of the seat-sharing group. A genetic algorithm is used to solve the
pre-allocation optimization problem, and a rule-based heuristic method
is introduced to generate the initial solution of the problem. The
results of the solution are verified by simulation experiments and
compared with other seat control modes.

(3) Research on dynamic pricing problem of high-speed railway based
on dynamic bid price

The dynamic pricing is an important mechanisms for the market operation
of railway passenger transportation. And the dynamic bid price mechanism
is one of the implementations of dynamic pricing methods. This paper
studies the seat inventory control model based on dynamic bid price
to determine dynamic price of railway tickets. Based on the modeling
framework, the optimal control problem and value function approximation
method are introduced. A dynamic programming model is proposed to
calculate the bid price. In problem solution, this paper firstly transforms
and simplifies the problem. In order to solve the large-scale linear
programming problem, a dynamic aggregation method and a column generation
method are proposed. The passenger's transfer behavior is also considered
and the impact of passenger transfer on the sales revenue of railway
passenger tickets is verified by numerical experiments.

(4) Research on railway dynamic price problem based on network flow
model

For the modeling of railway dynamic pricing problem, this paper also
considers the network-flow model, in which the passengers' travel
behavior and dynamic pricing mechanism are modeled as paths in the
state network. Thus a dynamic price strategy can be obtained by solving
a class of network path problems. To solve this kind of problem, this
paper studies the Lagrangian heuristic method. By using the Lagrangian
function decomposition method and the cutting plane method with trust
region, the problem can be solved rapidly in parallel. The numerical
experiments show that the proposed method can reduce the vibration
of the Lagrangian multipliers in the solution and stably approximate
the optimal solution.

(5) Case study of Nanning-Guangzhou High-speed Railway

In the background of the operation of Nanning-Guangzhou High-speed
Railway in 2016 summer, this paper tests different seat inventory
control mechanisms including ticket pre-allocation and dynamic pricing
in the varies demand scenarios. The results have shown that the flexible
use of stock keeping unit (SKU) and flexible pricing mechanism can
significantly increase ticket sales revenue.

\englishkeywords{High-Speed Railway \quad{}Revenue Management \quad{}Pre-allocation
\quad{}Dynamic Pricing \quad{}Markov Decision Process \quad{}Approximate
Dynamic Programming \quad{}Genetic Algorithm}
